This math problem

[Tempestknight]

Ok i have this math problem

Three boys, Josh, Hans, and Simon are sitting around on a farm with nothing to do. They walk into the barn and notice a scale used to weigh cattle. They decide to weigh themselves. Unfortunately, the scale begins at 100 kg. The problem is that none of them weigh more than 100 kg. They decide to weigh themselves in pairs. Josh was sure that he weighed the most.

Hans and Simon together = 132 kg.
Simon and Josh together = 151 kg.
Josh and Hans together = 137 kg.

What did they each weigh?

I have no clue all i know is that i have to isolate one variable
H = 132 - S
S = 151 - J
J = 137 - H
That is what the teacher told me i should start with, and after that i have no clue. I was wondering if anyone here could help me with this and tell me exactly what they did.

Thank you

David AKA Tempest

[manavo11]

H=132-S => H=132-(151-J) => H=132-(151-(137-H)) => H=132-(151-137+H) => H=132-151+137-H => 2*H=132-151+137

Find H, replace in the other ones.

[Tempestknight]

uh.... where the hell did the S go? ohhh ok i get it... But on
H=132-(151-137+H)

why positive H?

[manavo11]

When you take the minus and apply it to all the things in the parenthesis the sign of each item/thing (don't know the right word) changes. So -H becomes H when you remove the parenthesis and apply the minus in front of the parenthesis to the number and the variable H.

Moved to the Math forum from Chit Chat.

[Tempestknight]

ohhh ok so everything in the brackets is negative because of the - in front of it, ok i get it now. Thank you

[gigemboy]

S = 132 - (137 - (132 - S)) ...or not... i dunno

[manavo11]

Not 132 twice :

Hans and Simon together = 132 kg.
Simon and Josh together = 151 kg.
Josh and Hans together = 137 kg.

S = 151 - (137 - (132 - S))

Right?

[Tempestknight]

ya i made a mistake its S = 151-J but im figuring it out

[gigemboy]

yeah.. you made a mistake because something wasnt looking right.. YOUR fault.. HAHAHA! grrrrrrrrrr not my fault

[Tempestknight]

Ok sinse you started me off i got
H = 59
S = 73
J = 78
I think they are correct

[manavo11]

I got the same so it's correct

[Tempestknight]

Lol kinda sucks cause i never would have thought to go
H = 132-S
H = 132-(151-J)
If i got past that part on my own i would have been able to do the whole thing on my own

[manavo11]

Well, you had three equasions and three variables. That's all you need to find the value of all three. Just need to replace the right stuff

[sql_lall]

The easier way to think about it:
H + S = a
S + J = b
J + H = c
combining these gives: 2H + 2S + 2J = a + b + c
=> H + S + J = (a + b + c) / 2
now, say you want to find H:
H = H + S + J - (S + J) = (a + b + c) / 2 - b
the others are similar (note that a, b and c are given in the problem)